8 citations · 11 across the 10 of their papers we have counts for
11 papers
Strong Shape Invariance of Alexander-Spanier Normal Homology Theory
Anzor Beridze
In the paper [Ba-Be-Mdz], using the Alexander-Spanier cochains based on the normal coverings, the exact homology theory , the so called Alexander-Spanier homolo…
On the subgroup of that contains the kernel of Burau representation
A. Beridze, L. Davitadze
It is known that there are braids and in the braid group , such that the group is a fee subgroup \cite{7}, which contains the kernel of the B…
The Tautness Property of Homology Theory
Anzor Beridze, Leonard Mdzinarishvili
The tautness for a cohomology theory is formulated and studied by various authors. However, the analogous property is not considered for a homology theory. In this paper, we will d…
On Axiomatic Characterization of Alexander-Spanier Normal Homology Theory of General Topological Spaces
Vladimer Baladze, Anzor Beridze, Leonard Mdzinarishvili
The Alexandroff-Čech normal cohomology theory [Mor], [Bar], [Ba],[Ba] is the unique continuous extension \cite{Wat} of the additive cohomology theory [Mil], [Ber-Mdz$_1…
On the Universal Coefficient Formula and Derived Functor
Anzor Beridze, Leonard Mdzinarishvili
It is known that homology and inverse limit functors do not commute. In the paper we consider this very problem and find its application for various homology theories. In particula…
Strong Shape Theory of Continuous Maps
V. Baladze, A. Beridze, R. Tsinaridze
The work is motivated by the papers [Ba1], [Ba2], [Ba7], [Ba11], [Be] and [Be-Tu]. In particular, the strong homology groups of continuous maps were defined and studied in [Be] and…
On the Axiomatic Systems of Singular Cohomology Theory
Anzor Beridze, Leonard Mdzinarishvili
On the category of pairs of topological spaces having a homotopy type of complexes the singular (co)homology theory was axiomatically studied by J.Milnor. In particular, Milno…
On the Burau Representation of modulo
A. Beridze, S. Bigelow, P. Traczyk
The problem of faithfulness of the (reduced) Burau representation for is known to be equivalent to the problem of whether certain two matrices and generate a free gr…
Forks, Noodles and the Burau representation for
A. Beridze, P. Traczyk
\begin{abstract} The reduced Burau representation is a natural action of the braid group on the first homology group of a suitable infinite cy…
On the Axiomatic Systems of Steenrod Homology Theory of Compact Spaces
Anzor Beridze, Leonard Mdzinarishvili
On the category of compact metric spaces an exact homology theory was defined and its relation to the Vietoris homology theory was studied by N. Steenrod [S]. In particular, the ho…
Strong Homology Theory of Continuous Maps
Anzor Beridze, Vladimer Baladze
The current work is motivated by the papers , , , . In particular, using Theorem 3.7 of and methods developed in this paper, the spectral and s…